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There is a circular field with a radius of R1. A cow tethered on the circumference of this field with a rope length R2. What is the ratio of R1/R2 such that the cow grazes exactly half the area of the field. Mathematical proof please.

Answers

Wonderful ... IF the cow is tethered INSIDE the circle and at least R2 away from the circumference. But she is tethered ON the circumference. So part of the boundary of her grazing is an arc with radius R2, and the rest of the boundary is another arc with radius R1. This is not a simple situation.

The area she grazes is NOT a circle with radius equal to the length of the rope.